The Watford striker has confirmed he has made the decision over concerns for his family as the Premier League has allowed clubs to start training again ahead of the season resuming amid the coronavirus pandemic.
Speaking to Eddie Hearn and Tony Bellew on 'Talk the Talk' YouTube show, he said: "We're due back in this week. I've said I'm not going.
"It only takes one to get infected. I don't want to bring that home -- my son is five months and he's had breathing difficulties.
"I don't want to put him in more danger. You've got to drive back in the same dirty kit. If I'm putting my clothing in with my son's or my missus' it's more likely to be in the house.
"I've lost my Dad, my Gran, my Grandad... I've more or less everyone that I care about. So that, to me, is more important than a few quid in my back pocket."
Deeney claimed he didn't get the reassurances he needed from meetings with the Premier League.
He explained: "Within the meeting I asked very simple questions.
"For Black, Asian and mixed ethnicities they are four times more likely to get the illness and twice as likely to have long lasting illness.
"Is there any additional screening? Heart stuff to see if anyone has a problem? I just said 'If you don't know the information, why would I put myself at risk?' "